Selecting multiple vertices
What you described in your question is called proportional editing.  to enable/disable this, in edit mode, there is an icon that looks like this:

it is located towards the upper right corner.  When you click it, you can scroll your mouse up or down to make the area you want to edit bigger or smaller.  When you enable proportional editing and move a vertex, the circle you described in your question should appear.  If it doesn't, try scrolling your mouse wheel down until you can see it.  Hope this was helpful!